In the field of digital wireless communication, packet communication typified by Internet communication, and speech storage, the technique for encoding and decoding speech signals is essential for effectively utilizing transmission capacity of radio waves and storage media, and a large number of speech encoding and decoding schemes have been developed.
At present, a speech encoding and decoding scheme adopting a CELP scheme is put into practical use as a major stream (for example, Non-Patent Document 1). The speech coding scheme adopting the CELP scheme mainly stores models of vocalized sound and encodes input speech based on speech models stored in advance.
In recent years, in coding of speech signals and tone signals, a scalable coding technique is developed that applies the CELP scheme and makes it possible to decode speech and tone signals even from part of encoded information and suppress speech quality deterioration even when a packet loss occurs (for example, Patent Document 1).
A scalable coding scheme is generally formed with a base layer and a plurality of enhancement layers, and the layers form a layered structure with the base layer being the lowest layer. In each layer, a residual signal which is a difference between the input signal and output signal of a lower layer is encoded. According to this configuration, it is possible to decode speech and tone using encoded information of all layers or encoded information of a part of layers.
Further, in scalable coding, generally, the sampling frequency of the input signal is transformed, and the down-sampled input signal is encoded. In this case, the residual signal encoded by the higher layer is generated by up-sampling the decoded signal of the lower layer and calculating the difference between the input signal and the up-sampled decoded signal.    Patent Document 1: Japanese Patent Application Laid-Open No. HEI10-97295    Non-Patent Document 1: M. R. Schroeder, B. S. Atal, “Code Excited Linear Prediction: High Quality Speech at Very Low Bit Rate”, IEEE proc., ICASSP'85 pp.937-940